Ross et al.: Fundamentals
of Corporate Finance, Sixth
Edition, Alternate EditionIII. Valuation of Future
Cash Flows- Stock Valuation © The McGraw−Hill^275
Companies, 2002
You should start to notice that we can push the problem of coming up with the stock
price off into the future forever. It is important to note that no matter what the stock
price is, the present value is essentially zero if we push the sale of the stock far enough
away.^1 What we are eventually left with is the result that the current price of the stock
can be written as the present value of the dividends beginning in one period and ex-
tending out forever:
P 0 ...
We have illustrated here that the price of the stock today is equal to the present value
of all of the future dividends. How many future dividends are there? In principle, there
can be an infinite number. This means that we still can’t compute a value for the stock
because we would have to forecast an infinite number of dividends and then discount
them all. In the next section, we consider some special cases in which we can get around
this problem.
Some Special Cases
There are a few very useful special circumstances under which we can come up with a
value for the stock. What we have to do is make some simplifying assumptions about
the pattern of future dividends. The three cases we consider are the following: (1) the
dividend has a zero growth rate, (2) the dividend grows at a constant rate, and (3) the
dividend grows at a constant rate after some length of time. We consider each of these
separately.
Zero Growth The case of zero growth is one we’ve already seen. A share of common
stock in a company with a constant dividend is much like a share of preferred stock.
D 5
(1 R)^5
D 4
(1 R)^4
D 3
(1 R)^3
D 2
(1 R)^2
D 1
(1 R)^1
CHAPTER 8 Stock Valuation 245(^1) The only assumption we make about the stock price is that it is a finite number no matter how far away we
push it. It can be extremely large, just not infinitely so. Because no one has ever observed an infinite stock
price, this assumption is plausible.
Growth Stocks
You might be wondering about shares of stock in companies such as Yahoo! that currently pay
no dividends. Small, growing companies frequently plow back everything and thus pay no div-
idends. Are such shares worth nothing? It depends. When we say that the value of the stock
is equal to the present value of the future dividends, we don’t rule out the possibility that some
number of those dividends are zero. They just can’t allbe zero.
Imagine a company that has a provision in its corporate charter that prohibits the paying
of dividends now or ever. The corporation never borrows any money, never pays out any
money to stockholders in any form whatsoever, and never sells any assets. Such a corpora-
tion couldn’t really exist because the IRS wouldn’t like it; and the stockholders could always
vote to amend the charter if they wanted to. If it did exist, however, what would the stock be
worth?
The stock is worth absolutely nothing. Such a company is a financial “black hole.” Money
goes in, but nothing valuable ever comes out. Because nobody would ever get any return on
this investment, the investment has no value. This example is a little absurd, but it illustrates
that when we speak of companies that don’t pay dividends, what we really mean is that they
are not currentlypaying dividends.
EXAMPLE 8.1